Acceleration Curves. p K piston travel, N k o would be P's velocity on a time base. The ordinates at corresponding times are always the same, but the abscissae vary, and the two cases must be thoroughly grasped by the student. Acceleration Curves shew the rate at which the velocity is changing. Let a point move from A to B, Fig. 454, with changing velocity, as shewn by the <!urve AC B, AB being a distance base (here a necessity). Draw any tangent D E F and a normal E G, drop the perpendicular E H, and turn H G round to line H E, giving a point in the acceleration curve. Continuing the con- struction for various points, K L M is obtained, whose ordinates shew acceleration from A to L, and retardation from L to B. N.B.—If velocity and distance scales are the same, the ac- celeration may be measured to the same scale; but, if otherwise, and v = ft. per sec. of velocity to one inch, d = ft. distance to one inch, a new acceleration scale must be made, being the velocity scale, stretched or compressed in the ratio -. (See Appendix //., T) p. 863, for proof'; see also p. 674.) (See pp. 932, 1099, and 1106.) The Oscillating Lever is examined in Fig. 455. The virtual radii are drawn : w B a normal to the circumference, and p B perpendicular to w j. Then : vel. P B P "BW or as A D AW For AD being || to j B, the triangles WDA wj B are similar. Turning A D round to A c, we obtain one point in the polar curve, found as at Fig. 456, where ADW is right angle. W's velocity being uniform, the polar radii shew P's velocity. The centrode curve passes to infinity at K, N, G, and P, the direction of the dotted lines being at right angles to w p, when the latter is tan- gential to the crank circle, namely when P and W have uniform velocities. Whitworth's Quick-return Motion (Fig. 457).— B P being the driver, revolving uniformly, the angular and linear velocities of W are to be found. Produce p A to c and p B to D,